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Derivative from First Principle

If the roots ...

Question

If the roots of the equation $a x^{2} + x + b = 0$ be real and distinct, then the roots of the equation $x^{2} - 4 \sqrt{a b} x + 1 = 0$ will be-

rational

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real

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imaginary

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irrational

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Solution

The correct option is C imaginary
${a x}^{2} + x + b = 0 r o o t s a r e r e a l a n d d i s t i n c t ∴ D > 0 1 - 4 a b > 0$
$D_{1} = 4 a b - 1 = - D < 0 ∴ D_{1} < 0 s o r o o t s a r e i m a g i n a r y$

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